Wynn was surveyor general of mines in North Wales, constable of Caernarvon Castle, forester of Snowdon and steward of Bardsey from 1727 to 1761. He was appointed High Sheriff of Caernarvonshire for the year 1732 to 1733.
Wynn was returned as Member of Parliament (MP) for Caernarvonshire at a by-election on 2 January 1740. At the 1741 British general election he was returned instead for Denbigh Boroughs in a contest, followed by lengthy petition proceedings, which were ultimately decided in his favour. He was Deputy Cofferer of the Household from January to December 1743 and Deputy treasurer of Chelsea Hospital between 1741 and 1754. As the Chelsea Hospital post became incompatible with a seat in Parliament, he did not stand at the 1747 British general election.[3] He succeeded his father to the baronetcy on 13 April 1749.[1]